Identifying a short list of relevant documents of query \(Q\)  (or its de-contextualized form \(\hat{Q}\) ) from a large document collection \(\mathcal {D}\)  is computationally expensive. For efficiency, a coarse-to-fine search strategy is widely adopted where the overall search process is divided into two phases, document retrieval and ranking, either of which may consist of multiple steps to perform coarse-to-fine document retrieval or (re-)ranking, respectively.
Conceptually, document retrieval needs to examine each \(D \in \mathcal {D}\)  its relevance to \(Q\) . Since a brute-force method is prohibitively expensive,
it is necessary to construct an index of \(\mathcal {D}\)  for efficient retrieval.
For example, sparse retrieval methods (Section REF ) often use the (weighted) inverted index to help find the top-\(K\)  relevant documents efficiently, as that in ad hoc search [1]}.
Dense retrieval methods (Section REF , on the other hand, have to resort to efficient similarity search methods [2]}, [3]}, [4]} to find relevant documents in a continuous vector space.
